Analysis and Partial Differential Equations on Manifolds, Fractals and Graphs
Analysis and Partial Differential Equations on Manifolds, Fractals and Graphs

Author: Alexander Grigor'yan

Publisher: Walter de Gruyter GmbH & Co KG

Published: 2021-01-18

Total Pages: 526

ISBN-13: 311070076X

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The book covers the latest research in the areas of mathematics that deal the properties of partial differential equations and stochastic processes on spaces in connection with the geometry of the underlying space. Written by experts in the field, this book is a valuable tool for the advanced mathematician.

Analysis and Partial Differential Equations on Manifolds, Fractals and Graphs
Analysis and Partial Differential Equations on Manifolds, Fractals and Graphs

Author: Alexander Grigor'yan

Publisher: Walter de Gruyter GmbH & Co KG

Published: 2021-01-18

Total Pages: 337

ISBN-13: 3110700859

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The book covers the latest research in the areas of mathematics that deal the properties of partial differential equations and stochastic processes on spaces in connection with the geometry of the underlying space. Written by experts in the field, this book is a valuable tool for the advanced mathematician.

From Classical Analysis to Analysis on Fractals
From Classical Analysis to Analysis on Fractals

Author: Patricia Alonso Ruiz

Publisher: Springer Nature

Published: 2023-11-25

Total Pages: 294

ISBN-13: 3031378008

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Over the course of his distinguished career, Robert Strichartz (1943-2021) had a substantial impact on the field of analysis with his deep, original results in classical harmonic, functional, and spectral analysis, and in the newly developed analysis on fractals. This is the first volume of a tribute to his work and legacy, featuring chapters that reflect his mathematical interests, written by his colleagues and friends. An introductory chapter summarizes his broad and varied mathematical work and highlights his profound contributions as a mathematical mentor. The remaining articles are grouped into three sections – functional and harmonic analysis on Euclidean spaces, analysis on manifolds, and analysis on fractals – and explore Strichartz’ contributions to these areas, as well as some of the latest developments.

Geometric Potential Analysis
Geometric Potential Analysis

Author: Mario Milman

Publisher: Walter de Gruyter GmbH & Co KG

Published: 2022-06-21

Total Pages: 370

ISBN-13: 3110741717

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This monograph contains papers that were delivered at the special session on Geometric Potential Analysis, that was part of the Mathematical Congress of the Americas 2021, virtually held in Buenos Aires. The papers, that were contributed by renowned specialists worldwide, cover important aspects of current research in geometrical potential analysis and its applications to partial differential equations and mathematical physics.

The Sub-Laplacian Operators of Some Model Domains
The Sub-Laplacian Operators of Some Model Domains

Author: Der-Chen Chang

Publisher: Walter de Gruyter GmbH & Co KG

Published: 2022-08-01

Total Pages: 266

ISBN-13: 3110642999

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The book studies sub-Laplacian operators on a family of model domains in C^{n+1}, which is a good point-wise model for a $CR$ manifold with non-degenerate Levi form. A considerable amount of study has been devoted to partial differential operators constructed from non-commuting vector fields, in which the non-commutativity plays an essential role in determining the regularity properties of the operators.

Real Hypersurfaces in Hermitian Symmetric Spaces
Real Hypersurfaces in Hermitian Symmetric Spaces

Author: Jürgen Berndt

Publisher: Walter de Gruyter GmbH & Co KG

Published: 2022-04-04

Total Pages: 388

ISBN-13: 3110689839

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Hermitian symmetric spaces are an important class of manifolds that can be studied with methods from Kähler geometry and Lie theory. This work gives an introduction to Hermitian symmetric spaces and their submanifolds, and presents classification results for real hypersurfaces in these spaces, focusing on results obtained by Jürgen Berndt and Young Jin Suh in the last 20 years.

Heat Kernels and Analysis on Manifolds, Graphs, and Metric Spaces
Heat Kernels and Analysis on Manifolds, Graphs, and Metric Spaces

Author: Pascal Auscher

Publisher: American Mathematical Soc.

Published: 2003

Total Pages: 434

ISBN-13: 0821833839

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This volume contains the expanded lecture notes of courses taught at the Emile Borel Centre of the Henri Poincare Institute (Paris). In the book, leading experts introduce recent research in their fields. The unifying theme is the study of heat kernels in various situations using related geometric and analytic tools. Topics include analysis of complex-coefficient elliptic operators, diffusions on fractals and on infinite-dimensional groups, heat kernel and isoperimetry on Riemannian manifolds, heat kernels and infinite dimensional analysis, diffusions and Sobolev-type spaces on metric spaces, quasi-regular mappings and $p$-Laplace operators, heat kernel and spherical inversion on $SL 2(C)$, random walks and spectral geometry on crystal lattices, isoperimetric and isocapacitary inequalities, and generating function techniques for random walks on graphs. This volume is suitable for graduate students and research mathematicians interested in random processes and analysis on manifolds.

Graphs, Matrices, and Designs
Graphs, Matrices, and Designs

Author: Rees

Publisher: Routledge

Published: 2017-07-12

Total Pages: 350

ISBN-13: 1351444379

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Examines partitions and covers of graphs and digraphs, latin squares, pairwise balanced designs with prescribed block sizes, ranks and permanents, extremal graph theory, Hadamard matrices and graph factorizations. This book is designed to be of interest to applied mathematicians, computer scientists and communications researchers.